Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/abbaaaaa-aaaaaabbaaabb.srs)

The rewrite relation of the following TRS is considered.

a(b(b(a(a(a(a(a(x1)))))))) a(a(a(a(a(a(b(b(a(a(a(b(b(x1))))))))))))) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
a#(b(b(a(a(a(a(a(x1)))))))) a#(b(b(x1))) (2)
a#(b(b(a(a(a(a(a(x1)))))))) a#(b(b(a(a(a(b(b(x1)))))))) (3)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(b(b(x1)))) (4)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(b(b(a(a(a(b(b(x1))))))))) (5)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(a(b(b(x1))))) (6)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(a(b(b(a(a(a(b(b(x1)))))))))) (7)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(a(a(b(b(a(a(a(b(b(x1))))))))))) (8)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(a(a(a(b(b(a(a(a(b(b(x1)))))))))))) (9)
a#(b(b(a(a(a(a(a(x1)))))))) a#(a(a(a(a(a(b(b(a(a(a(b(b(x1))))))))))))) (10)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.